Human Dynamics: The Correspondence Patterns of Darwin and Einstein

While living in different historical era, Charles Darwin (1809-1882) and Albert Einstein (1879-1955) were both prolific correspondents: Darwin sent (received) at least 7,591 (6,530) letters during his lifetime while Einstein sent (received) over 14,500 (16,200). Before email scientists were part of an extensive university of letters, the main venue for exchanging new ideas and results. But were the communication patterns of the pre-email times any different from the current era of instant access? Here we show that while the means have changed, the communication dynamics has not: Darwin's and Einstein's pattern of correspondence and today's electronic exchanges follow the same scaling laws. Their communication belongs, however, to a different universality class from email communication, providing evidence for a new class of phenomena capturing human dynamics.Comment: Supplementary Information available at http://www.nd.edu/~network

Modelling the observed properties of carbon-enhanced metal-poor stars using binary population synthesis

The stellar population in the Galactic halo is characterised by a large fraction of CEMP stars. Most CEMP stars are enriched in $s$-elements (CEMP-$s$ stars), and some of these are also enriched in $r$-elements (CEMP-$s/r$ stars). One formation scenario proposed for CEMP stars invokes wind mass transfer in the past from a TP-AGB primary star to a less massive companion star which is presently observed. We generate low-metallicity populations of binary stars to reproduce the observed CEMP-star fraction. In addition, we aim to constrain our wind mass-transfer model and investigate under which conditions our synthetic populations reproduce observed abundance distributions. We compare the CEMP fractions and the abundance distributions determined from our synthetic populations with observations. Several physical parameters of the binary stellar population of the halo are uncertain, e.g. the initial mass function, the mass-ratio and orbital-period distributions, and the binary fraction. We vary the assumptions in our model about these parameters, as well as the wind mass-transfer process, and study the consequent variations of our synthetic CEMP population. The CEMP fractions calculated in our synthetic populations vary between 7% and 17%, a range consistent with the CEMP fractions among very metal-poor stars recently derived from the SDSS/SEGUE data sample. The results of our comparison between the modelled and observed abundance distributions are different for CEMP-$s/r$ stars and for CEMP-$s$ stars. For the latter, our simulations qualitatively reproduce the observed distributions of C, Na, Sr, Ba, Eu, and Pb. Contrarily, for CEMP-$s/r$ stars our model cannot reproduce the large abundances of neutron-rich elements such as Ba, Eu, and Pb. This result is consistent with previous studies, and suggests that CEMP-$s/r$ stars experienced a different nucleosynthesis history to CEMP-$s$ stars.Comment: 17 pages, 11 figures, accepted for publication on Astronomy and Astrophysic

An Algorithmic Test for Diagonalizability of Finite-Dimensional PT-Invariant Systems

A non-Hermitean operator does not necessarily have a complete set of eigenstates, contrary to a Hermitean one. An algorithm is presented which allows one to decide whether the eigenstates of a given PT-invariant operator on a finite-dimensional space are complete or not. In other words, the algorithm checks whether a given PT-symmetric matrix is diagonalizable. The procedure neither requires to calculate any single eigenvalue nor any numerical approximation.Comment: 13 pages, 1 figur

Statistical characterization of the forces on spheres in an upflow of air

The dynamics of a sphere fluidized in a nearly-levitating upflow of air were previously found to be identical to those of a Brownian particle in a two-dimensional harmonic trap, consistent with a Langevin equation [Ojha {\it et al.}, Nature {\bf 427}, 521 (2004)]. The random forcing, the drag, and the trapping potential represent different aspects of the interaction of the sphere with the air flow. In this paper we vary the experimental conditions for a single sphere, and report on how the force terms in the Langevin equation scale with air flow speed, sphere radius, sphere density, and system size. We also report on the effective interaction potential between two spheres in an upflow of air.Comment: 7 pages, experimen

How to Test for Diagonalizability: The Discretized PT-Invariant Square-Well Potential

Given a non-hermitean matrix M, the structure of its minimal polynomial encodes whether M is diagonalizable or not. This note will explain how to determine the minimal polynomial of a matrix without going through its characteristic polynomial. The approach is applied to a quantum mechanical particle moving in a square well under the influence of a piece-wise constant PT-symmetric potential. Upon discretizing the configuration space, the system is decribed by a matrix of dimension three. It turns out not to be diagonalizable for a critical strength of the interaction, also indicated by the transition of two real into a pair of complex energy eigenvalues. The systems develops a three-fold degenerate eigenvalue, and two of the three eigenfunctions disappear at this exceptional point, giving a difference between the algebraic and geometric multiplicity of the eigenvalue equal to two.Comment: 5 page

Characteristics of maize cultivars in Africa: how modern are they and how many do smallholder farmers grow?

Open Access Journal; Published online: 17 March 2017Maize is the most important cereal and most widely cultivated staple that plays a key role in the food security of sub-Saharan Africa (SSA). Although some countries have achieved significant gains in maize productivity, the SSA average yields are far below what could be obtained with improved cultivars under good crop management. Low cultivar turnover is one among many contributing factors to low maize yields in SSA. At present, there is a critical knowledge gap on the identity, number, and age of maize cultivars currently grown by smallholder farmers on the continent. Results This study revealed that nearly 500 maize cultivars were grown in 13 African countries surveyed in the 2013/2014 main crop season. Sixty-nine percent of the cultivars each occupied 40% and four occupied >30% area. Approximately 32% of all the cultivars were hybrids, 23% were improved open-pollinated varieties (OPVs), and 46% were locals. Eastern Africa (EA) and southern Africa (SA) accounted for about 43 and 38%, respectively, of all the cultivars reported, whereas West Africa’s (WA) share was 19%. The average area planted to modern cultivars in the surveyed areas was estimated at 57%—with EA, SA, and WA estimates of 82, 55, and 36%, respectively; however, increased adoption was not necessarily always related to improved productivity, as the latter depends on many additional factors. Each household planted an average of 1.781 cultivars (range 1–8). The overall weighted average age of the cultivars was 15 years, with hybrids and OPVs being 13 and 18 years, respectively. Conclusions Maize variety turnover in SSA is slower than what is practiced in the USA and other world regions such as Latin America and Asia. The substantial variations among regions and countries in all parameters measured suggest a tailored approach to mitigation interventions. Findings of this current study pave the way for replacing the old cultivars with more recent releases that are tolerant or resistant to multiple stresses and are more resilient

Holomorphic linearization of commuting germs of holomorphic maps

Let $f_1, ..., f_h$ be $h\ge 2$ germs of biholomorphisms of \C^n fixing the origin. We investigate the shape a (formal) simultaneous linearization of the given germs can have, and we prove that if $f_1, ..., f_h$ commute and their linear parts are almost simultaneously Jordanizable then they are simultaneously formally linearizable. We next introduce a simultaneous Brjuno-type condition and prove that, in case the linear terms of the germs are diagonalizable, if the germs commutes and our Brjuno-type condition holds, then they are holomorphically simultaneously linerizable. This answers to a multi-dimensional version of a problem raised by Moser.Comment: 24 pages; final version with erratum (My original paper failed to cite the work of L. Stolovitch [ArXiv:math/0506052v2]); J. Geom. Anal. 201

Highly efficient planar perovskite solar cells through band alignment engineering

The simplification of perovskite solar cells (PSCs), by replacing the mesoporous electron selective layer (ESL) with a planar one, is advantageous for large-scale manufacturing. PSCs with a planar TiO2 ESL have been demonstrated, but these exhibit unstabilized power conversion efficiencies (PCEs). Herein we show that planar PSCs using TiO2 are inherently limited due to conduction band misalignment and demonstrate, with a variety of characterization techniques, for the first time that SnO2 achieves a barrier-free energetic configuration, obtaining almost hysteresis-free PCEs of over 18% with record high voltages of up to 1.19 V

Transform-domain analysis of packet delay in network nodes with QoS-aware scheduling

In order to differentiate the perceived QoS between traffic classes in heterogeneous packet networks, equipment discriminates incoming packets based on their class, particularly in the way queued packets are scheduled for further transmission. We review a common stochastic modelling framework in which scheduling mechanisms can be evaluated, especially with regard to the resulting per-class delay distribution. For this, a discrete-time single-server queue is considered with two classes of packet arrivals, either delay-sensitive (1) or delay-tolerant (2). The steady-state analysis relies on the use of well-chosen supplementary variables and is mainly done in the transform domain. Secondly, we propose and analyse a new type of scheduling mechanism that allows precise control over the amount of delay differentiation between the classes. The idea is to introduce N reserved places in the queue, intended for future arrivals of class 1